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<title>Miniker 102 manual: 4.6 Generalized linear tangent system analysis</title>
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<ul class="toc"><li><a href="mini_ker.html#Top">Miniker 102 manual</a> </li>
<li><ul class="toc"><li><a href="Dynamic-system-analysis.html#Dynamic-system-analysis">4. Dynamic analysis of systems in Miniker</a> </li>
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<a name="Generalized-linear-tangent-system-analysis"></a>
<h2 class="section"> 4.6 Generalized linear tangent system analysis </h2>
<ul class="toc">
<li> <a href="#GTLS-with-cmz">4.6.1 Generalized tangent linear system with cmz</a> </li>
<li> <a href="#GTLS-with-make">4.6.2 Generalized tangent linear system with make</a> </li>
<li> <a href="#GTLS-run-and-output">4.6.3 Generalized tangent linear system analysis run and output</a> </li>
</ul>
<a name="index-Generalized-linear-tangent-system"></a>
<a name="index-GTLS"></a>
<a name="index-propagator"></a>
<a name="index-Lyapunov-exponents"></a>
<a name="index-sltcirc_002eexe"></a>
<p>The state matrix Ast may also be used to compute the
GTLS propagator (or state transition matrix applied to perturbation), after the simulation.
The algorithm is a finite product of
5th order development of
Φ(t + δt,t) = expAstδt.
Numerous element of analysis are given, in particular the determination
of the Lyapunov exponents of the system.
</p>
<p>An executable file, ‘<tt>sltcirc.exe</tt>’ is generated and running this file will
produce the corresponding results.
</p>
<hr size="2">
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<a name="Generalized-tangent-linear-system-with-cmz"></a>
<h3 class="subsection"> 4.6.1 Generalized tangent linear system with cmz </h3>
<a name="index-smod-1"></a>
<p>The cmz macro <code>smod SLTCIRC</code> prepares a main program
(‘<tt>circule</tt>’ of +PATCH SLTCIRC), in the directory ‘<tt>sltcirc/</tt>’.
</p>
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<a name="Generalized-tangent-linear-system-with-make"></a>
<h3 class="subsection"> 4.6.2 Generalized tangent linear system with make </h3>
<a name="index-Makefile_002esltcirc"></a>
<p>To compile the GTLS analysis executable with <code>make</code> you
can do
</p><table><tr><td> </td><td><pre class="example">make sltcirc.exe
</pre></td></tr></table>
<p>If you want to have a separate directory for the GTLS analysis, you should copy
the sequence ‘<tt>dimetaphi.inc</tt>’ (or make a link to that file) to the
directory. You should also copy the file ‘<tt>Makefile.sltcirc</tt>’ from the
‘<tt>template/</tt>’ directory in this directory and rename it ‘<tt>Makefile</tt>’
and set the Miniker directory path in the <code>miniker_dir</code> variable.
</p>
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<a name="Generalized-tangent-linear-system-analysis-run-and-output"></a>
<h3 class="subsection"> 4.6.3 Generalized tangent linear system analysis run and output </h3>
<a name="index-GTLS-run"></a>
<a name="index-run_002c-GTLS"></a>
<a name="index-GTLS-output"></a>
<a name="index-output_002c-GTLS"></a>
<a name="index-sltcirc_002eexe-1"></a>
<a name="index-title_002etex_002c-GTLS"></a>
<a name="index-dres_002edata_002c-GTLS"></a>
<a name="index-aspha_002edata_002c-GTLS"></a>
<p>The ‘<tt>sltcirc.exe</tt>’ executable generated by the compilation
computes the elements of analysis of the system. This program requires
‘<tt>title.tex</tt>’ to
transmit a title for output and graphics (see <a href="A-model-description.html#Title-file">Title file</a>),
‘<tt>aspha.data</tt>’ to access the
state matrix and ‘<tt>dres.data</tt>’, because time-step can be changed along the
simulation
(see <a href="Setting-and-running-a-model.html#Simulation-and-output">Running a simulation and using the output</a>)
<a name="DOCF10" href="mini_ker_fot.html#FOOT10">(10)</a>. To get access to these files
(in case they are not in the current
directory) it is possible to make a link to
the corresponding files in the model directory. Once it is done
the program may be run:
</p>
<table><tr><td> </td><td><pre class="example">./sltcirc.exe
</pre></td></tr></table>
<p>The following table gives the correspondence between variable name,
result file and ntuple number, with a short explanation:
</p>
<table>
<thead><tr><th>var</th><th>file</th><th>ntuple</th><th>explanation</th></tr></thead>
<tr><td><code>p(.,.)</code></td><td>‘<tt>phit.data</tt>’</td><td>55</td><td>propagator from 0 to t, Φ(t,0)</td></tr>
<tr><td><code>up(.,.)</code></td><td>‘<tt>uphit.data</tt>’</td><td>50</td><td>Left singular vectors U in the SVD of Φ</td></tr>
<tr><td><code>wp(.)</code></td><td>‘<tt>wphit.data</tt>’</td><td>51</td><td>singulat values w in the SVD of Φ</td></tr>
<tr><td><code>vp(.,.)</code></td><td>‘<tt>vphit.data</tt>’</td><td>52</td><td>Right Singular Vectors V in the SVD of Φ</td></tr>
<tr><td><code>wr(.)</code></td><td>‘<tt>wr.data</tt>’</td><td>53</td><td>real part of eigen values of Φ(t,0)</td></tr>
<tr><td><code>wi(.)</code></td><td>‘<tt>wi.data</tt>’</td><td>54</td><td>imaginary part of eigen values of Φ(t,0)</td></tr>
<tr><td><code>lwp(.)</code></td><td>‘<tt>lwphit.data</tt>’</td><td>67</td><td>Lyapunov exponents</td></tr>
</table>
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